Viscoelasticity means the simultaneous existence of viscous and elastic properties in a material. Many complex and structured fluids exhibit viscoelastic characteristics, i.e., they have the ability to both store energy like an elastic solid as well as dissipate energy such as a viscous liquid. When a stress is applied to such a viscoelastic fluid it stores some of the energy input, instead of dissipating all of it as heat and it may recover part of its deformation when the stress is removed.
The elastic modulus or G′ represents storage of elastic energy, while the loss modulus G″ represents the viscous dissipation of that energy. The magnitude of G′ and G″ for most complex fluids depends upon the time scales or frequency at which the property is probed. Depending upon the stress relaxation mechanisms present in the complex fluids, they may exhibit different behaviour (either G′>G″ or G″>G′ or G′=G″) at different frequencies. Having the ability to probe the viscoelastic response over a wide frequency range therefore provides insights into the stress-relaxation mechanisms in complex fluids, and since this is connected to the underlying structure of the complex fluid, insights into the underlying structure can be obtained.
Currently, high end rotational rheometers are used to measure these viscoelastic properties, but the measurement time can be quite long depending upon the frequency being probed. Also, a considerable amount of time can be spent in cleaning the rheometer's stage and preparing the test before the next sample can be loaded, making high-throughput measurements quite challenging. Other disadvantages of rotational rheometers include that they provide access to a very limited frequency range, and they require large sample volumes, typically greater than 1 ml.
Optical-based Microrheological techniques have also been used to measure viscoelastic properties of complex fluids. These involve embedding probe particles into a viscoelastic fluid of interest (polymer solution, surfactant solution etc.) and following the thermal motion of the probe particles. The thermally driven random motion of colloidal spheres suspended in a complex fluid is very different than the diffusive Brownian motion of similar spheres suspended in a purely viscous fluid (e.g simple Newtonian fluid). When suspended in complex fluids, which exhibit elasticity, the probe particles exhibit sub diffusive motion or if the elasticity becomes very significant the probe particles may become locally bound. As the microstructure slowly relaxes, it allows the particles to escape this elastic ‘cage.’ This motion of probe particles as a function of time can be obtained from mean squared displacement <Δr2(t)> of probe particles which can be obtained from the electric field autocorrelation function obtained from a Dynamic Light Scattering (DLS) experiment:
            g              (        1        )              ⁡          (      τ      )        =      exp    ⁡          (                        -                      1            6                          ⁢                  q          2                ⁢        Δ        ⁢                                  ⁢                              r            2                    ⁡                      (            τ            )                              )      
Once the mean squared displacement, <Δr2(t)> is obtained, it can be related through to the complex viscoelastic modulus G* and through to the elastic G′ and viscous modulus G″ through:G′(Ω)=|G*(Ω)|cos (πα(Ω)/2),G″(Ω)=|G*(Ω)|sin (πα(Ω)/2),
where
                        G        *            ⁡              (        ω        )                  ≈                              k          B                ⁢        T                    π        ⁢                                  ⁢        a        ⁢                  〈                      Δ            ⁢                                                  ⁢                                          r                2                            ⁡                              (                                  1                  /                  ω                                )                                              〉                ⁢                  Γ          ⁡                      [                          1              +                              α                ⁡                                  (                  ω                  )                                                      ]                                .  
This analysis is based on two key assumptions:                The system exhibits single scattering. As the system becomes multiply scattering the analysis no longer remains valid.        The scattering is dominated by the embedded probe particles, as the whole principle is based on following the motion of the embedded probe particles.        
Many complex fluids at even moderate concentrations start to contribute quite significantly to the scattered light signal. In order to ensure the domination of the scattering by probe particles, they need to be added in moderately high concentrations (but still much less than 0.5 vol %). Adding probe particles in these moderately concentrated regimes makes the system quite turbid and multiple scattering tends to become very significant.
In these types of systems, the concentration of probe particles can be raised even further to enter into the strongly multiply scattering regime, while changing the analysis from that described above to theories developed for using the multiply scattered light in the microrheological analysis. This then evolves into a technique known as Diffusing Wave Spectroscopy (DWS). An important concern for this technique is that the analysis is inherently complicated and makes interpretation of data highly challenging. The agreement of data obtained from DWS with mechanical data is in many cases quite poor and requires rescaling.